The technology disclosed herein relates to powertrains for vehicles. Japanese Unexamined Patent Publication No. 2006-9753 describes an example engine included in a powertrain for a vehicle. Specifically, Japanese Unexamined Patent Publication No. 2006-9753 describes a dynamic damper that is configured by spherical joints being provided in front of and behind purifiers (catalyst) for purifying an exhaust gas in an exhaust system for an engine.